136 IRE YRANSACTION9S ON ENGINEERING MANAGEMA11ENT Septeinberbasic idea urnderlyinig the enumerative cost model. When of investigators indicates that such comparability canthis is dlone cost and work accomplished are directly eventually be achieved. The work of Norden1719 andrelated and the previous ambiguity is avoided as showni Simon20 will aid in this respect. In the meantime, it isin Fig. 4. This in no way interferes with aggregation for more important to extend the application of activityreimbursement or departmnental cost control purposes. costing or enumerative cost models so that the basic dataIn addition, it provides the essential raw material for will be available for analysis.the colnstruction of time-cost relationships through 17 P. V. Norden, "Curve-fitting for a model of applied researchstatistical analysis (step 6). and development scheduling," IBMlI J. Res. & Dev., vol. 2, pp.

s ~ ~ * .P .232-48; July~, 1958.Onie further obstacle blocks the way of realizing the 18 P. V. Norden, "Internal dynamics of research and development

fulll potential of CPA. This is the fact that the actual time projects," Proc. 6th Annual Internat'l Meeting of the Inst. of Manage-f till potentia.-of CPA.This is the fact thattheactualtimement Sciences, Paris, France, September, 1958, Pergamon Press, Inc.,and cost for completioon of a given- activity yields only N. Y., N. YI.pp. 187-206 1960.one data point on the time-cost trade-off curve. Unless 19 P. V. Norden, "On the anatomy of development projects,"

IRE TRANS. ON ENGINEERING MANAGEMENT, vol. EM-7, pp. 30-42;some way is found to make data points from different March, 1960.activities comparable tlle time-cost curves ws-ill always T 20 C. K. Simon, "Standardization-the Key to Makinig PERTthe

. . . Work," presented at the First Joint Nat'l Meeting, ORSA-TIMS,remairn only estimates. PrelimiYnary analysis by a number San Francisco, Calif.; November, 1961.

Probabilistic Forecasting of Manpower Requirements*K. S. PACKARDt, SENIOR MEMBER, IRE

Summary-The use of the probability of a successful proposal inielude the very practical consideration that the prob-in manpower forecasts is discussed. Formulas for the expected ability of success is a function of the age of the proposal.requirements and the standard deviation are presented. An illus-trative example of the use of these formulas is given. DISCUSSION

INTRODUCTION An analysis of past experience has shownl that, for any

B USINESS forecasting, being a predictioni of the particular classification of proposal, the probability offuture is concerned with uncertain events. As such, success can be represented by a matrix similar to thatit is best handled by means of probabilities, shown in Table I. The elements of this typical matrix

provided that certain basic requirements are met. These represent the probability that a contract will result in

requirementsarh the nth month after submission if the proposal was

submitted in months ago (any other period could have1) There must be a reasonable quantity of separable been used instead of months). It should be recognized

events (sales). that the sum of any row is equivalenit to2) The events must be essentially interchangeable; n

that is, one is indifferent to which events occur, P Pp(M1i)so lonig as the quanitity is adequate.

The need for such a probabilistic approach is greatest in in Wadel and Bush', but that this quantity is a functionthose cases where the uncertainty is greatest. These of the length of time the proposal has been outstanding.conditions are met wheniever there is a large number This factor becomes of importance if, as is oftenl the case,of outstanding proposals, the volume of which is significanlt the response-time for receiving an ansswer is of the orderwith respect to the backlog. of the period for updating the forecast.A recent paper' by Wadel and Bush used a probabilistic The manpower requirements resulting from a successful

approach to the forecasting of manpower requirements proposal will generally follow a fixed pattern in timeresulting from successful proposals. The discussion starting at the contract date, but independelnt of when

following will treat the same problem, but will explicitly this date occurs in real time. This planned rate of workaccomplishment is known in advance, and together with

* Received Marc.h 15, 1962. the probability of success enables one to compute t-het Airborne Instruments Laboratory,? A Division of Cutler- expected2 manpower requirements.

HammSer, Inc., MelVille, L. I., N. Y.1 L. B. WVadel a.nd C. M. Bush, "'An approach to probabilistic The expected manpower requirement in the qth period

forecasting of engineering manpower requirements," IRE TRANS.ON ENGINEERING MANAGEMENT, VOl. EM-8, P. 158-159; September,1961. 2 "Expected" is used in the technical sense throughout.

1962 Packard: Forecasting of Manpower Requirements 137TABLE I. 7

PROBABILITY OF ACCEPTANCE OF A PROPOSAL n MONTHSAFTER SUBMISSION IF IT WAS SUBMITTED m MONTHS AGO.3 60

M\ 1 2 3 4 5_3

0 0.15 0.15 0.02 0.02 0.021 0.18 0.02 0.02 0.02 202 0.04 0.04 0.043 0.06 0.064 0.08

C'0 1 2 3 4 5 6 7 8 9 X 0 I1 12

MONTHS AFTER DATE OF CONTRACT

Fig. 1--Planned manpower requirements.from the present as a result of a specific proposal, say therth one is

ET[M(q)] = X,P-fQ-j+ (1) 0, 20

where °8W16

p= probability of success in the (m + j)th < 12

month following submission of a proposal FIOsubmitted m months ago, W 6

Mq-i+l = the planned manpower requirement in the 4

(qntract. afterreceiptofaJUL AUG SEPT OCT NOV DEC JAN FEB MAR APR MAY JUNEcontract.Fig. 2-Expected manpower requirements.

If we have n outstanding proposals m, p, and M willpossibly have different values for each proposal. Theexpected manpower requirement then becomes of simplicity, the standard deviation is the best choice;

n q that is,E[M(q)] = X Zpr(r).ryli+1(r) (2) rn q 1/2

r=1 i=1 D[ VI(q)] EE p(r)(r)f{M1 j+1(r) -Er[[M(q)] }2j. (3)This simple calculation will give the most accurate r=1 i=1

possible representation of what is to be expected, on the The probability that future results will fall within theaverage. standard deviation will depend on the form of the distribu-Whereas the expected work is a necessary factor tion. If, with more data available, the distribution can be

in planning, it is not sufficient. Consider the following fitted to some known functional form, then percentileexample: 2 outstanding proposals, each with a constant curves might be preferable to the standard deviation25 per cent chance of success, one requiring 4 men per for indicating dispersion.month the other requiring 100 men per month. Theexpected labor force is 26 men, but the only possibilities EXAMPLEare 0, 4, 100, and 104 men. In such a case to plan on To illustrate the application of this method, consider26 men might lead to disaster. This is an unfair example, a hypothetical proposal having an expenditure plan assince one would not use these techniques in such a simple shown in Fig. 1. Suppose that this is a type to whichcase, but it does illustrate a point. With a greater number the probabilities of Table I apply and that it has beenof outstanding proposals the expected value would also outstanding for one month, as of the first of July.be the most probable, but the probability that this value Since this sample proposal has been outstanding forwill be reached or exceeded is approximately 50 per cent 1 month, the m = 1 row is used in the computation.(the actual probability will depend on the distribution). The expected rate of expenditure is calculated from (1)To overcome this difficulty it is necessary to have some and is shown in Fig. 2. A similar computation would be

measure of the probable spread of the results. There are made for each outstanding proposal and the resultsseveral such measures, but it is believed that, for the sake added together. Although the expected value has little

meaning for a single proposal, it provides an accuratemeasure for a group of proposals.

3These data are applicable to a class of military R and D con- If one supposes that there are 100 outstanding proposalstracts. The reader should be warned, however, that such data varywidely with company marketing policies and with the customer, such as the one in the previous example then the expected

138 IRE TRANSl4ACTIONS ON ENGINEERING 1IANAGEM1JENT Septemnber

requiremenit E durin-g the month of iN\ovember, say, is probability matrices, such as is showni in Table I for each100 X 12.60 = 1260. The standard deviation D is found significant category of proposal. (The analysis must,to be 10 X 19.77 - 198. Because such a large number of course, include the determination of significantlyof similar proposals will result in a distribution that is different categories.) For ani automated system theseapproximately normal, it may be concluded that there probability matrices may be stored on punched tape,is anl 84 per cent chance that the requiiremenit will exceed for example, and periodically updated with currentE - D = 1062 during this moonth. This provides a experience. As each proposal is prepared, it would bereasonably firm basis for nmanpower planning, classified into onie of the categories and the plantned

if the number of proposals is reasonably large, the manpower requirements and date of submission wouldcomiiputations involved in u:sing this techniquie may be then be punched into a tape. A program would be preparedquite laborious and automatic data processing would be to compute (2) and (3) using the stored data. A periodicdesirable. In any event, the first step in implementing computation, say monthly, will provide a timely andthis technique is to analyze past performance to obtain accurate forecast of the expected manpower requirements.

The Razor's Edge of Support System Management*J1. W. VICK ROYt, SEN-IOR MEMBER, IRE

Summary-Two costly mistakes are frequently made in the is a very costly rework program of both hardwaremanagement of the support program for a major weapon or space and software to comply with prime system designsystem: 1) Considerations of support requirements are neglected hangesuntil it is too late to accomplish a reasonably scheduled minimum changcost program. 2) In an ardent effort to avoid the first mistake, These two mistakes can be eliminated by properhardware and software programs are promulgated before supportconcepts or prime system design have been adequately frozen. plngrand tin in the mementhof the supprtThe purpose of this paper is to illuminate these pitfalls and indicate program. The razor's edge between these two offers ahow they may be avoided. real challenge to the management of support requirements.

The purpose of this paper is to illuminate these pitfallsTV WO COSTLY mistakes are frequently made in the for management personnel not directly connected with

management of the support program for a major support, and in addition, to indicate how they may be

weapon or space systems. avoided. The support program is considered to include

1 Considerations of support requirements are neglected personnel, training, support equipment, spares, publica-tions and the aspects of prime system design that affect

until it is too late to accomplish a reasonablv. . . v ~~~~~~thesupport requirements.

scheduled minimum cost program. The result is a When the support program is not started early enough,crash program for the support requirements to the support management must work with a prime system"catch uip" wilth prime equipment program, which"calmostch alwithaprimeaequipmprogram,inwhic design that is essentially frozen. The usual result of this

situation is that the support hardware and software are

2) In an ardent effort to avoid the first mistake, unnecessarily complex. A good example of this situation is

hardware aiid software' programs are promulgated an amplifier in an aircraft servo system. This amplifierbefore support concepts or prime system design can be isolated as a malfunctioning item by two testhave been adequately frozen. The result of this points. The anomaly is that half of this unit is in the

Ioseof the aircraft and half in the tail fin; it takes four* Receivedl March 9, 1962. mr etpit n osdrbepyia aevrnt Radio Corporation of America, Burlington, Masse oets onsadcnidrbepyia aevrnThis term is used in the digital computer field. "Software,' as to determine which half iS at fault. This amplifier could

used in this paper, is meant to include maintenance manuals, operat- easily have been designed as one mechanical package ifing manuals, training programs. spares documwentation, support plan- supr reurmnshdbe osdrdbfrhnling (locuments, etc.supr eurmlthabenclsde efete